It's not your own driving you've got to worry about, it's everyone else's. What happens if some idiot pulls out in front of you and you need to make a very quick manoeuvre to avoid him, but because of your mixed tyres coupled with the dodgy weather and road conditions, the back end steps out unexpectedly and you spin 360? Now what if the same thing happens but there's a child on the pavement and you wipe them out with your spin?
Change them all and change them now. For the sake of a couple of hundred quid, it's just not worth it.
How would the back end step out if the rear had better tyres on it?